Using the SPDE approach for air quality mapping in Piemonte region

In this work we consider a geostatistical spatio-temporal model for PM10 concentration (particulate matter with an aerodynamic diameter of less than 10 µm) in the North-Italian region Piemonte. The model involves a Gaussian Field (GF) affected by a measurement error and a state process with a first order autoregressive dynamics and spatially correlated innovations. The main goal of this work is to propose an estimating and mapping strategy for such a model. This proposal is based on the work of Lindgren et al. (2011) that provides an explicit link between GFs and Gaussian Markov random fields (GMRF) through the Stochastic Partial Differential Equations (SPDE) approach. Thanks to the R library named INLA, the SPDE approach can be easily implemented providing results in reasonable computing time (with respect to other MCMC algorithms). For these reasons, the SPDE approach is proved to be a powerful strategy for modeling and mapping complex spatio-temporal phenomena.